Finite Group Databasebeta

← C5×C7×D5×D51 #49087938

Subgroups — C5×C7×D5×D51 #49087938

Order 35700.

192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C7×D5×C17C211yesmaximal, characteristic, complemented
2C52×C7×D51C211yesmaximal, characteristic, complemented
3C5×C7×D255C211yesmaximal, characteristic, complemented
4C5×C7×D5×D17—31nomaximal, Hall
5C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
6C2×C5×C7×D51—51nomaximal
7C7×D5×D51C511yesmaximal, characteristic, direct product factor
8C5×C7×D85—31no—
9C5×C7×D5×C17D311yescharacteristic, complemented
10C52×C7×D17—31no—
11C5×D5×D51C711yesmaximal, characteristic, direct product factor, Hall
12C7×D255C2×C511yescharacteristic, complemented
13C5×C7×D51—22no—
14C5×C7×D51—51no—
15C5×C7×D51D511yescharacteristic, direct product factor
16C5×C7×D51C2×C511yescharacteristic, complemented
17C3×C7×D5×C17C2×C511yescharacteristic, complemented
18C2×C3×C5×C7×C17—51no—
19C52×C7×C17C2×D311yescharacteristic, complemented, Hall
20C5×D255C2×C711yescharacteristic, complemented
21C52×D51C2×C711yescharacteristic, complemented
22C3×C5×D5×C17C2×C711yescharacteristic, complemented
23C2×C5×C7×D17—151no—
24C7×D5×D17—31no—
25C5×D3×C7×D5—171nomaximal, Hall
26C3×C5×C7×C17—22no—
27C3×C5×C7×C17C2×D511yescharacteristic, complemented
28C3×C5×C7×C17C22×C511yescharacteristic, complemented
29C5×D5×D17—31noHall
30C2×C7×D51—51noHall
31C3×C52×C17C22×C711yescharacteristic, complemented, Hall
32C2×C5×C7×C17—51no—
33C7×D85—31no—
34C7×D5×C17C5×D311yescharacteristic, complemented
35C5×C7×D17—31no—
36C5×C7×D17—31no—
37C5×C7×D17—62no—
38C5×C7×D17—151no—
39C5×C7×D15—171no—
40C52×D3×C7—171no—
41C3×C5×C7×D5D1711yescharacteristic, complemented
42C2×C5×D51—51no—
43D5×D51C5×C711yescharacteristic, direct product factor
44C5×D85—31no—
45C5×D5×C17D3×C711yescharacteristic, complemented
46C52×D17—31no—
47C2×C3×C7×C17—51no—
48C7×D51—51no—
49C7×D51C5×D511yescharacteristic, direct product factor
50C2×C5×C7×D5—511noHall
51C5×C7×C17—22no—
52C5×C7×C17D3×D511yescharacteristic, complemented
53C5×C7×C17C2×C5×D311yescharacteristic, complemented
54C3×C52×C7C2×D1711yescharacteristic, complemented, Hall
55C2×C3×C5×C17—51no—
56D255C2×C5×C711yescharacteristic, complemented
57C5×D51—22no—
58C5×D51—51no—
59C5×D51C7×D511yescharacteristic, direct product factor
60C5×D51C2×C5×C711yescharacteristic, complemented
61C3×D5×C17C2×C5×C711yescharacteristic, complemented
62C2×C7×D17—151noHall
63C52×C17C2×D3×C711yescharacteristic, complemented, Hall
64C2×C5×D3×C7—851no—
65D3×C7×D5—171no—
66C3×C7×C17C2×C5×D511yescharacteristic, complemented, Hall
67C2×C52×C7—511no—
68C5×C7×D5—511no—
69C5×C7×D5D5111yescharacteristic, direct product factor
70C2×C5×D17—151no—
71D5×D17—31no—
72C5×D3×D5—171noHall
73C3×C5×C17—22no—
74C3×C5×C17C2×C7×D511yescharacteristic, complemented
75C3×C5×C17C22×C5×C711yescharacteristic, complemented
76C2×C7×C17—51no—
77C7×D17—31no—
78C7×D17—151no—
79C2×C3×C5×C7—51no—
80C7×D15—171no—
81C5×D3×C7—171no—
82C5×D3×C7—171no—
83C5×D3×C7—342no—
84C5×D3×C7—851no—
85C3×C7×D5C5×D1711yescharacteristic, complemented
86C2×D51—51noHall
87C52×C7C2×D5111yescharacteristic, complemented, Hall
88C2×C5×C17—51no—
89D85—31no—
90C5×D17—31no—
91C5×D17—31no—
92C5×D17—62no—
93C5×D17—151no—
94D5×C17C5×D3×C711yescharacteristic, complemented
95C5×D15—171no—
96C52×D3—171no—
97C3×C5×D5C7×D1711yescharacteristic, complemented
98C22×C5×C7—2551no—
99C2×C7×D5—511no—
100C7×C17C5×D3×D511yescharacteristic, complemented, Hall
101C3×C5×C7—22no—
102C3×C5×C7D5×D1711yescharacteristic, complemented
103C3×C5×C7C2×C5×D1711yescharacteristic, complemented
104C2×C3×C17—51no—
105D51—51no—
106D51C5×C7×D511yescharacteristic, direct product factor
107C2×C5×D5—511noHall
108C5×C17—22no—
109C5×C17D3×C7×D511yescharacteristic, complemented
110C5×C17C2×C5×D3×C711yescharacteristic, complemented
111C2×D3×C7—851noHall
112C3×C52C2×C7×D1711yescharacteristic, complemented, Hall
113C2×C5×C7—51no—
114C2×C5×C7—511no—
115C2×C5×C7—511no—
116C2×C5×C7—1022no—
117C2×C5×C7—2551no—
118C7×D5—511no—
119C7×D5C5×D5111yescharacteristic, direct product factor
120C2×D17—151noHall
121C2×C5×D3—851no—
122D3×D5—171no—
123C3×C17C2×C5×C7×D511yescharacteristic, complemented, Hall
124C2×C52—511no—
125C5×D5—511no—
126C5×D5C7×D5111yescharacteristic, direct product factor
127C2×C3×C7—51no—
128D3×C7—171no—
129D3×C7—851no—
130C5×C7—22no—
131C5×C7D5×D5111yescharacteristic, direct product factor
132C5×C7C2×C5×D5111yescharacteristic, complemented
133C2×C17—51no—
134D17—31no—
135D17—151no—
136C2×C3×C5—51no—
137D15—171no—
138C3×D5C5×C7×D1711yescharacteristic, complemented
139C5×D3—171no—
140C5×D3—171no—
141C5×D3—342no—
142C5×D3—851no—
143C22×C7—2551noHall
144C52C2×C7×D5111yescharacteristic, complemented, Sylow
145C3×C7C5×D5×D1711yescharacteristic, complemented, Hall
146C22×C5—2551no—
147C2×D5—511no—
148C17C5×D3×C7×D511yescharacteristic, complemented, Sylow
149C3×C5—22no—
150C3×C5C7×D5×D1711yescharacteristic, complemented
151C3×C5C2×C5×C7×D1711yescharacteristic, complemented
152C2×C7—51no—
153C2×C7—511no—
154C2×C7—2551no—
155C2×D3—851noHall
156C2×C5—51no—
157C2×C5—511no—
158C2×C5—511no—
159C2×C5—1022no—
160C2×C5—2551no—
161D5—511no—
162D5C5×C7×D5111yescharacteristic, direct product factor
163C7C5×D5×D5111yescharacteristic, direct product factor, Sylow
164C2×C3—51no—
165D3—171no—
166D3—851no—
167C5—22no—
168C5C7×D5×D5111yescharacteristic, direct product factor
169C5C2×C5×C7×D5111yescharacteristic, complemented
170C22—2551noSylow
171C3C5×C7×D5×D1711yescharacteristic, complemented, Sylow
172C2—51no—
173C2—511no—
174C2—2551no—
subgroupG/H
center, hypercenterC5×C7D5×D51
commutator, cosocle, hypocenterC3×C5×C17C22×C5×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C17C22
LCSG ▷ C3×C5×C17
UCSC1 ◁ C5×C7

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×C5×C7×D5×C17C2semidirect
2. C52×C7×D51C2semidirect
3. C5×C7×D255C2semidirect
5. C3×C52×C7×C17C22semidirect
7. C7×D5×D51C5direct (N × H)
9. C5×C7×D5×C17D3semidirect
11. C5×D5×D51C7direct (N × H)
12. C7×D255C2×C5semidirect
15. C5×C7×D51D5direct (N × H)
16. C5×C7×D51C2×C5semidirect
17. C3×C7×D5×C17C2×C5semidirect
19. C52×C7×C17C2×D3semidirect
20. C5×D255C2×C7semidirect
21. C52×D51C2×C7semidirect
22. C3×C5×D5×C17C2×C7semidirect
27. C3×C5×C7×C17C2×D5semidirect
28. C3×C5×C7×C17C22×C5semidirect
31. C3×C52×C17C22×C7semidirect
34. C7×D5×C17C5×D3semidirect
41. C3×C5×C7×D5D17semidirect
43. D5×D51C5×C7direct (N × H)
45. C5×D5×C17D3×C7semidirect
49. C7×D51C5×D5direct (N × H)
52. C5×C7×C17D3×D5semidirect
53. C5×C7×C17C2×C5×D3semidirect
54. C3×C52×C7C2×D17semidirect
56. D255C2×C5×C7semidirect
59. C5×D51C7×D5direct (N × H)
60. C5×D51C2×C5×C7semidirect
61. C3×D5×C17C2×C5×C7semidirect
63. C52×C17C2×D3×C7semidirect
66. C3×C7×C17C2×C5×D5semidirect
69. C5×C7×D5D51direct (N × H)
74. C3×C5×C17C2×C7×D5semidirect
75. C3×C5×C17C22×C5×C7semidirect
85. C3×C7×D5C5×D17semidirect
87. C52×C7C2×D51semidirect
94. D5×C17C5×D3×C7semidirect
97. C3×C5×D5C7×D17semidirect
100. C7×C17C5×D3×D5semidirect
102. C3×C5×C7D5×D17semidirect
103. C3×C5×C7C2×C5×D17semidirect
106. D51C5×C7×D5direct (N × H)
109. C5×C17D3×C7×D5semidirect
110. C5×C17C2×C5×D3×C7semidirect
112. C3×C52C2×C7×D17semidirect
119. C7×D5C5×D51direct (N × H)
123. C3×C17C2×C5×C7×D5semidirect
126. C5×D5C7×D51direct (N × H)
131. C5×C7D5×D51direct (N × H)
132. C5×C7C2×C5×D51semidirect
138. C3×D5C5×C7×D17semidirect
144. C52C2×C7×D51semidirect
145. C3×C7C5×D5×D17semidirect
148. C17C5×D3×C7×D5semidirect
150. C3×C5C7×D5×D17semidirect
151. C3×C5C2×C5×C7×D17semidirect
162. D5C5×C7×D51direct (N × H)
163. C7C5×D5×D51direct (N × H)
168. C5C7×D5×D51direct (N × H)
169. C5C2×C5×C7×D51semidirect
171. C3C5×C7×D5×D17semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×C5×C7×D5×C172
C52×C7×D512
C5×C7×D2552
C5×C7×D5×D173
C2×C5×C7×D515
C7×D5×D515
C5×D5×D517
C5×D3×C7×D517